eVidyarthi

Main Menu
  • eVidyarthi
  • School
    • Class 6th
      • Maths Class 6
      • Science Class 6
      • Hindi Class 6
      • व्याकरण
      • English Class 6
      • English Grammar
      • Sanskrit Class 6
      • Geography
      • Civics
      • History
    • Class 7th
      • Maths Class 7
      • Science Class 7
      • Hindi Class 7
      • व्याकरण
      • English Class 7
      • English Grammar
      • Sanskrit Class 7
      • Geography
      • Civics
      • History
    • Class 8th
      • Maths Class 8
      • Science Class 8
      • Hindi Class 8
      • व्याकरण
      • English Class 8
      • English Grammar
      • Sanskrit Class 8
      • Geography
      • Civics
      • History
    • Class 9th
      • Maths Class 9
      • Science Class 9
      • Hindi Class 9
      • English Class 9
      • English Grammar
      • व्याकरण
      • Economics Class 9
      • Geography Class 9
      • Civics Class 9
      • History Class 9
    • Class 10th
      • Maths Class 10
      • Science Class 10
      • Hindi Class 10
      • English Class 10
      • English Grammar
      • व्याकरण
      • Economics Class 10
      • History Class 10
      • Civics Class 10
      • Geography Class 10
    • Class 11th
      • Maths Class 11
      • Accounts Class 11
      • English Class 11
      • English Grammar
      • व्याकरण
      • Chemistry Class 11
      • Physics Class 11
      • Biology Class 11
    • Class 12th
      • Maths Class 12
      • Accounts Class 12
      • Chemistry Class 12
      • Physics Class 12
      • Biology Class 12
      • English Class 12
      • English Grammar
      • व्याकरण
    • Close
  • English
    • Basic English Grammar
    • Basic English Speaking
    • English Vocabulary
    • English Idioms & Phrases
    • Personality Enhancement
    • Interview Skills
    • Close
  • Softwares
    • Microsoft Word
    • PhotoShop
    • Excel
    • Illustrator
    • PowerPoint
    • Close
Class 8th Maths || Menu
  • Important
    • Sample Paper – I
    • Sample Paper – II
    • Important Formulas
    • Revision Notes
    • MCQs
    • Mathematics Book
    • Close
  • Rational Numbers
    • Ex 1.1
    • Ex 1.2
    • MCQs
    • Ex 1.1 NCERT Solutions
    • Ex 1.2 NCERT Solutions
    • Close
  • Linear Equations in One Variable
    • Ex 2.1
    • Ex 2.2
    • Ex 2.3
    • Ex 2.4
    • Ex 2.5
    • Ex 2.6
    • MCQs
    • Ex 2.1 NCERT Solutions
    • Ex 2.2 NCERT Solutions
    • Ex 2.3 NCERT Solutions
    • Ex 2.4 NCERT Solutions
    • Ex 2.5 NCERT Solutions
    • Ex 2.6 NCERT Solutions
    • Close
  • Understanding Quadrilaterals
    • Ex 3.1
    • Ex 3.2
    • Ex 3.3
    • Ex 3.4
    • MCQs
    • Ex 3.1 NCERT Solutions
    • Ex 3.2 NCERT Solutions
    • Ex 3.3 NCERT Solutions
    • Ex 3.4 NCERT Solutions
    • Close
  • Practical Geometry
    • Ex 4.1
    • Ex 4.2
    • Ex 4.3
    • Ex 4.4
    • Ex 4.5
    • MCQs
    • Ex 4.1 NCERT Solutions
    • Ex 4.2 NCERT Solutions
    • Ex 4.3 NCERT Solutions
    • Ex 4.4 NCERT Solutions
    • Ex 4.5 NCERT Solutions
    • Close
  • Data Handling
    • Ex 5.1
    • Ex 5.2
    • Ex 5.3
    • MCQs
    • Ex 5.1 NCERT Solutions
    • Ex 5.2 NCERT Solutions
    • Ex 5.3 NCERT Solutions
    • Close
  • Squares & Square Root
    • Ex 6.1
    • Ex 6.2
    • Ex 6.3
    • Ex 6.4
    • MCQs
    • Ex 6.1 NCERT Solutions
    • EX 6.2 NCERT Solutions
    • Ex 6.3 NCERT Solutions
    • Ex 6.4 NCERT Solutions
    • Close
  • Cubes and Cube Roots
    • Ex 7.1
    • Ex 7.2
    • MCQs
    • Ex 7.1 NCERT Solutions
    • Ex 7.2 NCERT Solutions
    • Close
  • Comparing Quantities
    • Ex 8.1
    • Ex 8.2
    • Ex 8.3
    • MCQs
    • Ex 8.1 NCERT Solutions
    • Ex 8.2 NCERT Solutions
    • Ex 8.3 NCERT Solutions
    • Close
  • Algebraic Expressions and Identities
    • Ex 9.1
    • Ex 9.2
    • Ex 9.3
    • Ex 9.5
    • MCQs
    • Ex 9.1 NCERT Solutions
    • Ex 9.2 NCERT Solutions
    • Ex 9.3 NCERT Solutions
    • Ex 9.4 NCERT Solutins
    • Ex 9.5 NCERT Solutions
    • Close
  • Visualising Solid Shapes
    • Ex 10.1
    • Ex 10.3
    • MCQs
    • Ex 10.1 NCERT Solutions
    • Ex 10.2 NCERT Solutions
    • Ex 10.3 NCERT Solutions
    • Close
  • Mensuration
    • Ex 11.1
    • Ex 11.2
    • Ex 11.3
    • Ex 11.4
    • MCQs
    • Ex 11.1 NCERT Solutions
    • Ex 11.2 NCERT Solutions
    • Ex 11.3 NCERT Solutions
    • Ex 11.4 NCERT Solutions
    • Close
  • Exponents and Powers
    • Ex 12.1
    • Ex 12.2
    • MCQs
    • Ex 12.1 NCERT Solutions
    • Ex 12.2 NCERT Solutions
    • Close
  • Direct and Inverse Proportions
    • Ex 13.1
    • Ex 13.2
    • MCQs
    • Ex 13.1 NCERT Solutions
    • Ex 13.2 NCERT Solutions
    • Close
  • Factorisation
    • Ex 14.1
    • Ex 14.2
    • Ex 14.3
    • Ex 14.4
    • MCQs
    • Ex 14.1 NCERT Solutions
    • Ex 14.2 NCERT Solutions
    • Ex 14.3 NCERT Solutions
    • Close
  • Introduction to Graphs
    • Ex 15.1
    • Ex 15.2
    • Ex 15.3
    • MCQs
    • Ex 15.1 NCERT Solutions
    • Ex 15.2 NCERT Solutions
    • Ex 15.3 NCERT Solutions
    • Close
  • Playing with Numbers
    • Ex 16.1
    • Ex 16.2
    • MCQs
    • Ex 16.1 NCERT Solutions
    • Ex 16.2 NCERT Solutions
    • Close

CBSE Class 8 Maths Chapter 4 Practical Geometry Notes

To construct a quadrilateral uniquely, it is necessary to have the knowledge of at least five of its parts.

Five necessary parts to construct a quadrilateral may be:

  1. four sides and diagonal
  2. Three sides and two diagonals
  3. Four sides and an angle
  4. Three sides and two included angles
  5. Two adjacent sides and three angles

To construct a rhombus:

  1. Draw a diagonal of a given length and draw perpendicular bisector of this diagonal base.
  2. Take half of the given measurement of second diagonal and cut off arcs on either side of the perpendicular bisector. It will give two points of a rhombus.
  3. Join these points with the points on the first diagonal. It will give the required rhombus.

Before constructing a quadrilateral, one must draw a rough sketch of given measurements.

Trapezium, rhombus, and square are different forms of a parallelogram.

A rhombus can be a parallelogram, but a parallelogram cannot be a rhombus.

A square and a rhombus both have equal sides and a square can be rhombus but a rhombus cannot be a square.

We have learned the procedure of drawing triangles in the preceding class. We know that three measurements (of sides and angles) are required to draw a unique triangle. Here, we shall investigate whether four measurements are sufficient to draw a quadrilateral or not.

Constructing A Quadrilateral
We shall learn how to draw a unique quadrilateral when the following measurements are given:

  • four sides and one diagonal
  • two diagonals and three sides
  • two adjacent sides and three angles
  • three sides and two included angles
  • other special properties.

When the Lengths of Four Sides and a Diagonal are given
In this case we divide the quadrilateral into two triangles which can be easily drawn with the help of the given measurements.
Suppose that we are to construct the quadrilateral ABCD. Then two cases arise:

  • Diagonal AC is given: Here we divide the quadrilateral ABCD into two triangles ABC and ADC which can be easily drawn.
  • Diagonal BD is given: Here we divide the quadrilateral ABCD into two triangles ABD and BCD which can be easily drawn.

When Two Diagonals and Three Sides are given
In this case, we draw any one of the two diagonals. It determines two vertices of the quadrilateral. Then taking two suitable sides of the three sides, we locate the third vertex of the quadrilateral. Finally using the second diagonal and the remaining side, we locate the fourth vertex of the quadrilateral.

When Two Adjacent Sides and Three Angles are Known
We know that the sum of the angles of a quadrilateral is 360°. Since the three angles are given, therefore, if need be, the measure of the fourth angle can be readily obtained.

Thus, the angle between two adjacent sides is known if it is not even already given.
To construct the quadrilateral, we first draw two adjacent sides with the included angle between them. Then, at the other extremities of the adjacent sides, we draw rays at the given angles so as to intersect at a vertex (fourth) of the quadrilateral.
Thus the quadrilateral can be drawn completely.
Practical Geometry Class 8 Notes Maths Chapter 4

When Three Sides and Two included Angles are Given
We specifically note the three sides and the two included angles. First, we draw the common side of the two angles. At its extremities, we draw the other sides of the given angles with their given measures. In the last, we join the extremities of the other two sides. Thus, we can draw the quadrilateral completely.

Some Special Cases
There are certain specific quadrilaterals which can be constructed with less number (<5) of available measurements.

Android App

eVidyarthi

Search On eVidyarthi

Evidyarthi on Facebook

Like us on Facebook

Follow Evidyarthi on Youtube

Learn English
Learn English Through हिन्दी
Job Interview Skills
English Grammar
हिंदी व्याकरण - Vyakaran
Mathematics Class 6th
Science Class 6th
हिन्दी Class 6th
Mathematics Class 7th
Science Class 7th
हिन्दी Class 7th
हिन्दी Class 8th
Mathematics Class 8th
Mathematics Class 9th
English Class 9th
Science Class 9th
Mathematics Class 10th
English Class 10th
Mathematics Class XI
Chemistry Class XI
Accountancy Class 11th
Accountancy Class 12th
Mathematics Class 12th
Microsoft Word
Microsoft Excel
Microsoft PowerPoint
Adobe PhotoShop
Adobe Illustrator
Learn German
Learn French
IIT JEE
Privacy Policies, Contact Us
Copyright © 2020 eVidyarthi and its licensors. All Rights Reserved.